Lemma 3 ( [1]}) 
Let \(d\)  and \(M\)  be positive integers. Let \(f,g \in \mathbb {Z}[x_1, \ldots , x_d]\)  be relatively prime and define
\(S_M(f,g) = \lbrace  a \in \mathbb {Z}^d \mid f(a) \equiv g(a) \equiv 0 \mod {p} \ \text{for some prime} \ p >M\rbrace .\) 
